A method for calculating the current density of charged particle beams and the effect of finite source size and spherical and chromatic aberrations on the focusing characteristics

Abstract

A method for calculating current density of a focusing system including the effects of finite source size, spherical, and chromatic aberrations is presented. Current density at the target plane can be determined by calculating the origin of trajectories at the object plane, for each target point. The relation between object and image points is calculated by numerical integration of the ray equation and using the analytical results from geometrical aberration theory. The focusing characteristics for current density distributions are also investigated. A focusing position which gives the maximum axial current density does not give a good beam current profile (measured by a knife edge) in the case of large aberrations, because the aberrations cause the current distribution to have a long tail.